## Exam-Style Questions on Quadratic Equations## Problems on Quadratic Equations adapted from questions set in previous Mathematics exams. |

## 1. | IGCSE Extended |

(a) Show that the equation \(\frac{3}{x+1}+\frac{3x-9}{2}=1\) can be simplified to \(3x^2-8x-5=0\).

(b) Solve the equation \(3x^2-8x-5=0\) showing all of your working and giving answers to three significant figures.

(c) The total surface area of a cone with radius \(x\) and slant height \(8x\) is equal to the area of a circle with radius r. Show that \(r = 3x\).

[The curved surface area, \(A\), of a cone with radius \(r\) and slant height \(l\) is \(A=\pi rl\).]

## 2. | IB Studies |

A red rug has a width of \(x-3\) cm and a length of \(4x\) cm.

(a) Write down an ex^{2}, of the rug.

The area of the rug is 3240 cm^{2}.

(b) Calculate the value of \(x\).

(c) Hence, write down the value of the length and of the width of the rug in centimetres.

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